Podcast
Questions and Answers
What is the meaning of the Greek root word 'gonia'?
What is the meaning of the Greek root word 'gonia'?
What is a polygon?
What is a polygon?
What is the sum of the lengths of the sides of a two-dimensional body called?
What is the sum of the lengths of the sides of a two-dimensional body called?
What is a regular hexagon composed of?
What is a regular hexagon composed of?
Signup and view all the answers
What is the measure of each interior angle of a regular hexagon?
What is the measure of each interior angle of a regular hexagon?
Signup and view all the answers
What is the sum of all the interior angles of a hexagon?
What is the sum of all the interior angles of a hexagon?
Signup and view all the answers
What is the characteristic of an irregular hexagon?
What is the characteristic of an irregular hexagon?
Signup and view all the answers
What is the characteristic of a convex hexagon?
What is the characteristic of a convex hexagon?
Signup and view all the answers
What is the characteristic of a concave hexagon?
What is the characteristic of a concave hexagon?
Signup and view all the answers
What is an example of a complex hexagon?
What is an example of a complex hexagon?
Signup and view all the answers
Study Notes
Definition of a Hexagon
- A hexagon is a two-dimensional shape with six sides and six interior angles.
- The term "hexagon" comes from Greek roots "hex" meaning "six" and "gonia" meaning "corner".
Features of a Hexagon
- A hexagon is a polygon, a two-dimensional, closed geometrical shape made up of straight line segments.
- It has six equal sides and angles, making it a regular polygon.
Regular Hexagons
- A regular hexagon has six equal line segments making six equal angles.
- All sides and angles of a regular hexagon are equal in dimension.
- The perimeter of a regular hexagon is the sum of all its sides.
- Each interior angle of a regular hexagon measures 120 degrees.
- A regular hexagon is equiangular, meaning all angles have equal measure.
Angles of a Regular Hexagon
- A regular hexagon can be thought of as consisting of six identical equilateral triangles.
- Each angle of a regular hexagon has two angles of an equilateral triangle, each measuring 60 degrees.
Formula for the Area of a Regular Hexagon
- The formula for the area of a regular hexagon is (3 * sqrt(3) * a^2) / 2, where a is the side length of the hexagon.
- Another formula for the area of a regular hexagon is (3 * (a^2 * sqrt(3)) / 4), where a is the side of the hexagon and d is the height of the hexagon from one of the bases.
Irregular Hexagons
- An irregular hexagon is one that does not have six equal sides and six equal angles.
- Not all sides and angles of an irregular hexagon have to have different measures.
Features of Irregular Hexagons
- All interior angles of an irregular hexagon do not measure 120 degrees.
- All exterior angles of an irregular hexagon do not measure 60 degrees.
- The perimeter of an irregular hexagon is not given by a simple formula, but rather by adding individual side lengths.
Convex Irregular Hexagons
- A convex hexagon is a hexagon with an outward curved design, where all interior angles are less than 180 degrees.
Concave Irregular Hexagons
- A concave hexagon is a hexagon with one or more surfaces curved inwards, where at least one interior angle is greater than 180 degrees.
Complex Hexagons
- Complex hexagons are six-sided, closed structures formed by the intersection of different shapes, such as the Star of David.
Hexagons in Nature
- Hexagons exist naturally in the formation of snowflakes, the crystalline structure of graphene, and in the honeycombs made by bees.
- Hexagonal rocks can sometimes occur naturally, and the center scutes on a turtle's carapace are also hexagonal in shape.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Learn about the definition and features of hexagons, including their polygon properties and regular hexagon characteristics.
